# Mie scattering

As Mie scattering or Lorenz - Mie scattering refers to the elastic scattering of electromagnetic waves of spherical objects, the diameter of which corresponds approximately to the wavelength of the radiation. It was named after the German physicist Gustav Mie and the Danish physicist Ludvig Lorenz.

## Description

The Mie theory is the exact solution of Maxwell's equations for the scattering of a plane electromagnetic wave on a spherical object ( any size). In this case, the incident plane wave and the scattered electromagnetic field is described in a series of radiating spherical wave functions. The internal field is developed into regular spherical wave functions. Then the expansion coefficients of the scattered field and thus the scattered electromagnetic field can be calculated at any point in space using the boundary conditions on the sphere surface. In his essay of 1908 Mie succeeded the mathematical description of the color effects of a suspension of colloidal gold nanoparticles. Furthermore, it can be concluded with simple methods on the size and the refractive index of a microscopic particle by means of the Mie theory in particle measurement technology. The characteristic depending on the angle fluctuating in space scattered light can also be understood as an interference of the diffracted wave on the body. This intensity distribution of the scattering in the space is absorbed. It can be calculated back on the properties of the particle.

For small objects (object diameter) Mie scattering can be approximated by the Rayleigh scattering for large objects ( object diameter ) approaches the Mie theory of classical (geometric) solution to the refraction at a ball. Therefore, it is often called Mie scattering, when the diameter of the object is in this border region between Rayleigh scattering and classical scattering.

We are talking about the scattering by air molecules as Rayleigh scattering, only to emulsified fat droplets as Mie scattering, although all cases are in falling raindrops and floating Nebeltröpfen as classical scattering and accurately described by the Mie theory. In practice, you can solution the three cases well separated from each other by the different degree of polarization and the scattering distribution:

- Rayleigh scattering: strongly dependent on wavelength, linearly polarized with perpendicular scattering, symmetric scattering back and forth
- Mie scattering: light depends on the wavelength, light to medium polarized in the vertical scattering, slightly asymmetrical scattering to complex scattering distributions
- Classical (geometric ) scattering at small droplets: not wavelength dependent, non-polarized, no longer detectable limited scattering angle in the forward direction ( halo formation ), complex scattering distributions by varying the droplet size
- Classical (geometric ) scattering at large drops: not wavelength dependent, non-polarized, very limited scattering angle, so that halo formation is absent

The Mie scattering has a meaning also in radio technology. Thus, the reflection and the radar cross-section of metal parts can be calculated, its scope is in the range of the radio waves. The effective reflecting surface of a metal sphere with a diameter of one third of the wavelength is nearly four times what would be expected according to classical scattering. Further, smaller maxima occur at integer multiples of the circumference to the wavelength.